Band-gap renormalization in carbon nanotubes:: Origin of the ideal diode behavior in carbon nanotube p-n structures

We demonstrate dramatic modifications to the electronic structure in single-walled carbon nanotubes due to band gap renormalization, the many-body induced shrinkage of the fundamental band gap. This is examined within the framework of ideal p-n diodes formed along individual single-walled carbon nanotubes. A combination of photocurrent spectroscopy with detailed transport measurements provides a complete set of energy levels of the nanotube p-n structure. These energy levels confirm the large band gap shrinkage, consistent with enhanced many-body correction in one-dimensional confinement, and result in fundamental changes to the nanotubes diode transport properties as compared to their bulk counterparts. We show that the ideal diode behavior is a direct consequence of significant renormalization of the band gap at the doped p and n regions, resulting in formations of heterointerfaces, in stark contrast to a uniform band gap expected of a homogeneous material.